Piezoresistive and capacitive sensors are being used in increasingly higher accuracy applications for sensing various changes in pressure and the like in a variety of environments. Because the output of these sensors typically varies over temperature, the sensors require compensation and calibration in order to achieve the accuracy and temperature stability requirements of these applications. The calibration of sensors typically requires the adjustment of four parameters to achieve optimum output performance over temperature--offset, offset temperature coefficient (OTC), signal gain, and gain temperature coefficient (GTC).
In general the transfer function of a sensor is given by: EQU Vsens=Offset.sub.0 .multidot.(1+.alpha..sub.1 .multidot.T+.alpha..sub.2 .multidot.T.sup.2 + . . . +.alpha..sub.n .multidot.T.sup.n)+S.sub.0 .multidot.(1+.beta..sub.1 .multidot.T+.beta..sub.2 .multidot.T.sup.2 + . . . +.beta..sub.n .multidot.T.sup.n).multidot.Q Equation 1
where:
Vsens is the sensor output voltage PA1 Offset.sub.0 is the sensor offset (output with zero excitation) at a reference temperature (e.g. 25.degree. C.) PA1 .alpha..sub.1 is the first order temperature coefficient of the sensor offset PA1 .alpha..sub.2 is the second order temperature coefficient of the sensor offset PA1 .alpha..sub.n is the n.sup.th order temperature coefficient of the sensor offset PA1 T is the temperature difference from the reference temperature PA1 S.sub.0 is the sensor sensitivity or span at the reference temperature (e.g. 25.degree. C.) PA1 .beta..sub.1 is the first order temperature coefficient of the sensor sensitivity PA1 .beta..sub.2 is the second order temperature coefficient of the sensor sensitivity PA1 .beta..sub.n is the n.sup.th order temperature coefficient of the sensor sensitivity PA1 Q is the physical parameter being sensed (e.g. pressure, acceleration, etc.) PA1 Vout is the calibrated sensor output voltage (output of conditioning circuit) PA1 Gain.sub.0 is the gain of the compensating amplifier at the reference temperature PA1 Voff is the offset added by the conditioning circuit PA1 Votc.multidot.T is the temperature dependent component of the offset added by the conditioning circuit PA1 .delta. is the temperature dependent component of the gain of the compensating amplifier which counteracts the temperature dependent component of the sensor sensitivity PA1 Voff=-Offset.sub.0 PA1 Votc=-Offset.sub.0 .multidot..alpha..sub.1 PA1 and .delta.=-.beta..sub.1
For most sensor applications, all but the first order terms can be ignored so that Equation 1 becomes: EQU Vsens=Offset.sub.0 .multidot.(1+.alpha..multidot.T)+S.sub.0 .multidot.(1+.beta..multidot.T).multidot.Q Equation 2
However, for high accuracy sensor applications, the second order terms are usually included so that Equation 1 becomes: EQU Vsens=Offset.sub.0 .multidot.(1+.alpha..sub.1 .multidot.T+.alpha..sub.2 .multidot.T.sup.2)+S.sub.0 .multidot.(1+.beta..sub.1 .multidot.T+.beta..sub.2 .multidot.T.sup.2).multidot.Q Equation 3
To compensate this signal, a signal conditioning circuit is required which must subtract out the offset terms and provide amplification which varies with temperature to counteract the effect of the sensor span (TC). Traditionally, the signal conditioning has been done with opamps and laser trimmed resistors. However, this type of signal conditioning circuit is usually limited to providing first order correction of the temperature dependent terms. In addition this method is expensive as it requires the use of a laser and the solution is typically not monolithic (on a single integrated circuit) as the opamps and resistors are usually built on separate substrates.
An embodiment of a conventional digital compensation circuit 100 is shown in FIG. 1. In this embodiment, the differential signal from the sensor 5' is fed into an amplifier 102 which may have a gain of 1 or greater depending on the application. The output of this amplifier is fed into another amplifier stage 104 whose gain is controlled by the contents of a gain register 106. In addition, the offset and offset TC terms are added at summation point 114 in this stage using DACs 108, 110, 112 controlled by digital parameters. The compensation of the sensor sensitivity TC is done in the third stage 116 after the offset, offset TC and gain compensation. The third stage 116 may also have a gain of 1 or greater depending on the application. The final stage is an output buffer 111.
In this circuit, the temperature, T, is sensed using an on-chip proportional to absolute temperature (PTAT) circuit 122. The analog signal representing T is digitized using an analog-to-digital converter 124. The digital word representing T is then used to control two DACs 110 and 120, one for the offset TC compensation and the other for the gain TC compensation Digital information representing the values of the compensation terms, is serially fed into an on-chip control unit 125. The individual bits are decoded and sent to the various DACs 108, 110, 112, and 118. Once the correct binary code has been selected to center the sensor characteristic in the specified range, the code is stored using a digital storage method such as zener-zap, EEPROM or fuse link. The transfer function of this circuit 100 is given by Equation 4. EQU Vout=(Vsens+Voff+Votc.multidot.T).multidot.Gain.sub.0 .multidot.(1+.delta..multidot.T) Equation 4
Combining equations 3 and 4 gives: EQU Vout=S.sub.0 .multidot.Q.multidot.(1+.beta..sub.1 .multidot.T+.beta..sub.2 .multidot.T.sup.C)+Offset.sub.0 .multidot.(1+.alpha..sub.1 .multidot.T+.alpha..sub.2 .multidot.T.sup.2).multidot.+Voff+Votc.multidot.T.multidot.!.multidot.Gain .sub.0 .multidot.(1+.delta..multidot.T) Equation 5
The calibration of the sensor involves making measurements of Vout at various values of Q and various temperatures and thereby deducing the values of Voff, Votc, Gain.sub.0 and .delta. to minimize the error between Vout and the ideal sensor characteristic. Ideally the Voff, and Gain.sub.0 terms would be found first using measurements at the initial calibration temperature at minimum and maximum Q. The temperature dependent terms would then be found by an additional set of measurements at high (or low) temperature.
By setting:
equation 5 becomes: EQU Vout=S.sub.0 .multidot.Q.multidot.Gain.sub.0 .multidot.1+T.sup.2 .multidot.(.beta..sub.2 +.delta..multidot..beta..sub.1).sub.2 +T.sup.3 .multidot..delta..multidot..beta..sub.2 !+Offset.sub.0 .multidot..alpha..sub.2 .multidot.Gain.sub.0 .multidot.(1+.delta..multidot.T).multidot.T.sup.2 Equation 6
The desired term is simply S.sub.0 .multidot.Q.multidot.Gain.sub.0. All the other terms arise because this circuit only corrects for linear variations of the sensor offset and sensitivity with temperature. In high accuracy applications these extra terms may limit the usability of the sensor since it may be impossible to calibrate the sensor within the desired specification.
Accordingly, what is needed is a system and method to allow for more accurate calibration of sensors. The system and method should be easy to implement and cost effective. The present invention addresses such a need.